Experimental study on the significance of pressure relief effect and crack extension law under uniaxial compression of rock-like materials containing drill holes

The drilling pressure relief technology is an effective way to reduce the accumulation of elastic energy in the tunnel envelope, which can reduce the risk of regional ground pressure occurrence. However, there is a lack of theoretical guidance on which drilling parameter has the greatest degree of influence on the effectiveness of pressure relief. The uniaxial compression tests were conducted to study the relationships between drilling parameters (the diameter, depth, and spacing) and the mechanical properties and deformation modulus of specimens. The results show that: (1) The drilling diameter (DDR) and drilling depth (DDH) of single-hole specimens negatively correlate with the peak-failure strength and deformation modulus, while the drilling spacing (DS) of double-hole specimens positively correlates with the peak-failure strength and deformation modulus. It shows that the borehole diameter has a more significant effect on the decompression effect. (2) With the help of the Grey Relational Analysis, the factors affecting the peak-failure strength and deformation modulus of the drilled specimens were ranked in significance. From the largest to the smallest, they are DDR, followed by DDH and DS. (3) The role of the pressure relief mechanism is to transfer the high stress in the shallow part of the roadway to the deep part, reduce the peak strength of destruction and deformation modulus of the peripheral rock in the drilled section, so that the characteristics of the mechanical behavior of the rock are significantly weakened, and the range of the area of the drilled hole decompression is enlarged. During the loading of the borehole, the borehole stress field dominates in the early stage, and cracking starts near the borehole along the direction perpendicular to the direction of maximum principal stress (horizontal direction). In the later stage, the maximum principal stress field dominates and vertical cracks with large widths appear. During crack expansion, the plastic energy dissipation effect is enhanced and the deep impact conduction path is weakened, thus protecting the roadway. This study determined the significance of the pressure relief effect of different drilling parameters, which can guide reasonable modifications of drilling parameters in the field.


Drilling pressure relief principle
The radius of a single borehole pressure relief zone is mainly affected by vertical stress, lateral pressure coefficient, surrounding rock cohesion, internal friction angle, and borehole radius 42 .Only borehole parameters can be manually changed for underground mining activities, so the influence of borehole parameters on specimen strength, deformation modulus, and failure characteristics can be studied through laboratory tests.
The excavation of the roadway broke the equilibrium state of the original rock stress field 43 , and after the stress redistribution, the surrounding rock formed a fracture zone, plastic zone, and elastic stress elevation zone (elastic zone), as shown in Fig. 2b from shallow to deep.The junction of the plastic zone and the elastic stress elevation zone is the location of the peak stress, as shown in curve 1 in Fig. 2a.After constructing multiple boreholes inside the roadway, the borehole surrounding rock also formed a fracture zone, a plastic zone, and an elastic stress elevation zone from shallow to deep due to the redistributed stress.When multiple borehole fracture zones and plastic zones interact, a large pressure relief circle forms in the roadway's pressure relief section.The reduction of the bearing capacity of the surrounding rock led to the transfer of high stress from the shallow part to the deep part, and the stress at the original peak position was reduced, as shown in curve 2 in Fig. 2a, to achieve pressure relief.

Materials
Sand, cement, and gypsum were selected as similar materials for proportioning.The bulk density was γ = 18 kN/ m 3 .The aggregate was naturally graded ordinary river sand, and the natural gradation was as listed in Table 1.The cement was white silicate cement grade 325.Gypsum was a common gypsum powder.The 9 # coal mechanical parameters are shown in Table 2.The similarity ratio of capacity to weight was calculated as C γ = 12.3/18 = 0.68.The similarity ratio of stress was calculated as C σ = C l × C γ = 10 × 0.68 = 6.8, and the uniaxial compressive strength of the test model design was C c = C coal × C σ = 35.79/6.8= 5.26 MPa.Multiple groups of similar material proportioning tests were conducted to determine the mass ratio of cement: gypsum: water: sand as 1:3:3.5:10.

Methods
Figure 3 shows the experimental process and equipment.The specific steps are given as follows: • The geometric similarity ratio of the model test was taken as follows.The length, width, and height of the model were 100 mm × 100 mm × 100 mm.The holes were reserved inside the model, and the horizontal displacement of the fixed specimen was fixed during the test.• The control variable method was used.Combined with the site construction situation, the three parameter sizes differ by 1 ~ 2 orders of magnitude, so the similarity ratios cannot be consistent.For the special case of drilling depth of 6 ~ 24 m (coal pillar side), the commonly used drilling spacing is 1.5 ~ 2 m, and the drilling diameter is 100 ~ 300 mm, so the similarity ratios are determined to be 10 for the drilling diameter (DDR), 300 for the drilling depth (DDH), and 50 for the drilling spacing (DS).Three specimens of the same size were tested in each group.The specific research plan is given as follows.
(3) To study the effect of borehole depth, the specimen contained only a single hole with a fixed borehole diameter of 10 mm and borehole depths of 20 mm, 40 mm, 60 mm, or 80 mm.Name them in order as H1-1, H1-2, H1-3 … H4-2, H4-3.(4) To study the effect of borehole spacing, the specimens were tested with double holes, with a fixed borehole diameter of 10 mm, a borehole depth of 100 mm and borehole spacing of 30 mm, 35 mm, 40 mm, or 45 mm.Name them in order as S1-1, S1-2, S1-3 … S4-2, S4-3.A specimen was taken from each group to make a test protocol, and the details are shown in Table 3. • A layer of cling film was wrapped around the outer wall of the PVC pipe, which had different diameters.
It was fixed inside the mold according to the experimental design scheme, after which it was poured.The  specimens were demolded 48 h after production, and the PVC pipe with cling film was removed with tools and placed in the laboratory for support.• The test loading unit adopted C64.106/1000 kN electro-hydraulic servo universal testing machine, and the control unit adopted Test Expert.NET control software with a sampling frequency of 20 Hz.The test model horizontal displacement restraint device consists of two high-strength horizontal restraint steel plates, four M10 restraint steel rods, and M10 hexagonal nuts.The test was loaded at a rate of 0.8 mm/min until the post-peak strength of the specimen model was 70%.The test process was filmed with a high-speed camera at a recording speed of 50 frames/s.

Results and discussion
Effects of drilling parameters on the specimens failure strength and deformation modulus The absolute deviation (the absolute deviation of each test result from the mean value), relative deviation (the ratio of the absolute deviation to the mean value), standard deviation and relative standard deviation of the mean values for each drilling parameters are also provided in Tables 4, 5, 6, 7, 8, 9 to examine the reproducibility of the test results.The above data were also plotted in Figs. 7, 10, 13.Both the relative deviation and relative standard deviation in Tables 4, 5, 6, 7, 8, 9 are lower than 15% with the maximum relative deviation and the maximum coefficient of deviation being 13.98% (Specimen number H 1-2 in Table 7) and 9.92% (Test Scenario DDR = 25 mm in Table 5) respectively.The deviation values are within acceptable limits and prove the reproducibility of the test results 44 .The values in each test scenario in Tables 4, 5, 6, 7, 8, 9 are used in the following sections to study the effect of drilling parameters on specimen peak strength and specimen deformation modulus.

DDR
(1) Tables 4 and 5    (2) With the increasing drilling diameter, the peak-failure strength and the deformation modulus of the specimen decreases, and overall both of them are negatively correlated with the drilling diameter.The fitting functions are σ = − 0.0995d dr + 5.742, and E = − 0.00054d dr 2 − 0.00026d dr + 0.87.The values of the goodness of fit are 0.999 and 0.979, respectively, and the goodness of fit is fine.
(3) When the diameter of the borehole exceeds 15 mm, the stress-strain curves of large diameter specimens are more likely to enter the yielding stage during loading, and the weakening effect of strength is more obvious.this was also confirmed by Huang 45 investigated the acoustic emission (AE) characteristics of specimens at different borehole diameters and found that the AE activity before the peak strength point was stronger when the borehole diameter was larger, resulting in the bearing capacity of the specimens is also significantly weaker.This further indicates that larger diameter boreholes produce more damage to the interior of the rock mass, resulting in a significant weakening of the rock mechanical behavior characteristics.It is also demonstrated that the larger diameter borehole creates a wider range of pressure relief area, which can better achieve stress transfer and reduce the impact hazard [46][47][48] .(3) In a comprehensive view, as the drilling depth and the unloading range continues to increase, the stressstrain curve of the specimen is more likely to enter the yielding stage during the loading process, and the weakening effect on the mechanical properties of the rock is more significant.and the deformation modulus continues to grow, but overall both of them are positively correlated with the drilling spacing.The fitting functions are σ = 0.044d s + 2.55, and E = 0.0018d s 2 − 0.11d s + 2.2.The values of the goodness of fit are 0.912 and 0.863, respectively, and the goodness of fit is fine.When the hole distance exceeds 35 mm, the growth rate of the deformation modulus of the drilled specimen is faster, which indicates that the stress state of the specimen is changed and the overall strength is increased.
(3) With the increase of drilling spacing, the stress value required for the specimen to enter the yielding stage continues to increase, indicating that the smaller spacing has a better effect on the weakening of rock mechanical properties, and the stress fields in the drilling holes affect each other, forming a larger unloading area.

Significance analysis
The above test data were extracted for 36 sets of peak-failure strength and deformation modulus data of drilled specimens, with the intact specimens used as the control group.The correlation between each influencing factor and the peak-failure strength and deformation modulus of drilled specimens was quantitatively calculated using Grey Relational Analysis.The significance of each influence on the peak-failure strength and deformation modulus of drilled specimens was determined, as listed in Table 10.

Dimensionless variables
The sequences were homogenized, and the formulae were calculated as shown below:

Calculate the correlation degree
The absolute difference series of the comparison sequence and the reference sequence were found separately, and the two levels of the maximum difference and two levels of the minimum difference were found.The calculation is shown below: The maximum difference and minimum difference of the sequence are: The formula for calculating the correlation coefficient between x 0 (k) and x i (k) is: where ζ is usually taken as = 0.5, and the average value of the calculated correlation coefficient is taken as the correlation between the reference sequence and the comparison sequence, calculated as follows: The peak-failure strength grey correlation degrees are: γ (x 0 , x 1 ) = 0.810846; γ (x 0 , x 2 ) = 0.801637; γ (x 0 , x 3 ) = 0.515757.
The calculated correlations are listed in Table 11, and the correlations causing changes in the peak-failure strength and deformation modulus of the drilled specimens are ranked the drilling diameter (DDR) being the highest, followed by DDH and DS.
The DDR has the most significant impact on the peak-failure strength and deformation modulus of the specimens, followed by the depth and spacing.In practical engineering applications, the diameter and depth of drilling holes can be adjusted according to the basic situation of the site to achieve a better pressure relief effect.

DDR
(1) As seen from Fig. 14, damage to the specimen is mainly spalling, crack expansion, and specimen skin drop damage in the inner wall of the borehole.All specimens with different borehole diameters show tensile www.nature.com/scientificreports/cracks due to the stress concentration around the borehole, and transverse cracks are formed from the borehole outward with the increasing load in the vertical direction [49][50][51] .Figure 14a shows that the connection between the initiating crack and the borehole is weak for a borehole diameter of 10 mm. Figure 14b shows that at a borehole diameter of 15 mm, the initiating crack is produced near the borehole, and inner wall spalling occurs.Multiple cracks connected to the borehole extend deeper into the specimen, but the crack width is small, and small tensile cracks are produced around the borehole in addition to the main crack.When the diameter of the borehole is 20 mm, debris flaking and the falling phenomenon are more  prominent, the crack is more clearly defined, and the crack width increases (Fig. 14c).Figure 14d shows that the cracks were produced earlier, and the main crack width continued to grow at a borehole diameter of 25 mm.(2) During the compression of the specimen, it is mainly affected by the main stress field and the borehole stress field, and with the increase of vertical load, the borehole stress field is superimposed on the main stress field, which mainly shows that the damage occurs in the borehole structure and cracks in the direction perpendicular to the maximum main stress (horizontal direction), and subsequently expands along the direction of the maximum main stress.(3) Overall, as the diameter of the borehole increases, the tiny cracks gradually disappear and evolve into a smaller number of cracks with larger widths and lengths.When the DDR exceeds 15 mm, the damage pat-  www.nature.com/scientificreports/tern of the specimen changes, and fissures start to develop away from the borehole extension.It indicates that the specimens are mainly influenced by the main stress field and the influence of the borehole stress field is gradually weakened.

DDH
(1) As seen in Fig. 15, the main damage form of the specimen is still crack expansion and epidermal drop.Among them, the specimens with greater hole depths have tensile cracks due to stress concentration around the borehole.With the increasing load in the vertical direction, macro cracks are formed through the borehole outward, while the cracks in the borehole with smaller hole depth mainly appear in the distant part of the borehole.Figure 15a shows that the connection between the starting crack and the borehole is not close when the borehole depth is 20 mm, and the cracks mainly develop at the distal part of the borehole.Figure 15b shows that initiation cracks form around the borehole at a hole depth of 40 mm, but the cracks are relatively inconspicuous and small in width.Tensile cracks are also produced far from the borehole area.Figure 15c shows that at a hole depth of 60 mm, in addition to the main crack, small tensile cracks form around the hole, and the cracks gradually expand deeper.Figure 15d shows that at a hole depth of 80 mm, there is a main crack through the hole and the specimen, and the width of the crack is larger.(2) When the borehole depth is small, the borehole morphology is relatively intact, and the damage of the specimen occurs mainly on the sides away from the borehole.As DDH increases (more than 40 mm), the cracks keep approaching the borehole, and longitudinal cracks begin to appear near the borehole and gradually penetrate.It indicates that the influence of the borehole stress field gradually weakened and the main stress field began to dominate.

DS
(1) As seen in Fig. 16, the primary damage forms of the specimens remain crack expansion and skin drop.The specimen with smaller spacing produces cracks around the borehole and between the two boreholes.With the increase of vertical load, cracks start along the direction perpendicular to the maximum principal stress (horizontal direction), and the cracks gradually expand and form transverse cracks through the two holes, indicating that the stress fields of the two boreholes are superimposed at this time.In contrast, the two-hole specimen with a larger spacing produces cracks only around the borehole and gradually expands to form macroscopic cracks that do not interfere.Figure 16a shows that when the DS is 30 mm, a through macro crack is produced between the two boreholes, and the crack width is greater compared to other spacing, resulting in overall structural damage of the specimen, called "through-type" damage.(2) Fig. 16b shows that at a spacing of 35 mm, a through macroscopic crack is produced between the two boreholes.However, the crack width is smaller than 30 mm. Figure 16c shows that at a spacing of 40 mm, cracks are produced between the two boreholes, but there is no penetration.As the load increases, the specimen is damaged, called "independent-penetration transition type" damage.Figure 16d shows that when the distance between the boreholes is 45 mm, the two boreholes are independent, and the interaction between the two holes is small.No through cracks are produced between the boreholes, and the cracks around the respective boreholes are far apart.As the load increases, structural damage to the specimen is caused, called "independent" damage.It also indicates that the influence range of the borehole stress field is about 1.5-2 times the borehole diameter.(3) Comparing the damage patterns of specimens with different hole spacings, as the hole spacing increases, the independence of the two boreholes continues to increase, and the mutual influence of each borehole continues to decrease.The transverse crack between the two boreholes continues to decrease until it disappears.An "independent-penetration transition" damage forms in the 40 mm borehole spacing specimens.At this time, the pressure relief of the large diameter borehole has the least influence on the anchorage area of the surrounding rock, which can achieve the organic unification of the pressure relief effect and anchorage strength.The longitudinal cracks on both sides of the specimen continue to increase, indicating that the main stress field dominates at this time.
The vertical load provided by the testing machine was defined as the maximum principal stress in a vertical downward direction.As shown in Fig. 17a, when the depth of the borehole is large enough (100 mm), the crack initially starts in the horizontal direction of the borehole (perpendicular to the direction of the maximum principal stress), and the length of the horizontal crack is small, and the final morphology of the crack is consistent with the direction of the maximum principal stress.As shown in Fig. 17b, the crack initiation direction is still perpendicular to the direction of the maximum principal stress, and the cracks can be connected with each other when the spacing of the boreholes is small, and the horizontal cracks are longer, and the final morphology of the cracks is also consistent with the direction of the maximum principal stress.It can be seen that the initial crack expansion is more adequate when the stress fields of the boreholes are superimposed on each other.
The mechanism of pressure relief works to transfer the high stress in the shallow part of the roadway to the deep part, reduces the peak-failure strength of the surrounding rock in the drilling section, and changes the deformation modulus.After drilling, cracks are generated around the borehole, the plastic zone of the surrounding rock of the borehole is closed, the plastic energy dissipation effect is enhanced, and the deep impact conduction path is weakened to protect the roadway.

Conclusions
(1) Using the Grey Relational Analysis, the factors affecting the peak-failure strength and deformation modulus of drilled specimens were ranked in order of significance.The factors affecting the peak-failure strength and deformation modulus of drilled specimens in descending order were drilling diameter (DDR), followed by drilling depth (DDH), and drilling spacing (DS).(2) The DDR, DDH, and DS all show primary linear functions with the peak-failure strength.The DDR and DDH of single-hole specimens negatively correlate with the peak-failure strength.When more cracks are produced around the drill holes, a more complete release of strain energy of the specimen occurs.The DS of double-hole specimens and the peak-failure strength are positively correlated.As the spacing between the boreholes continues to increase, the specimen changes from "through" damage to "independent" damage, the influence between the boreholes decreases, and the strain energy released decreases.

Figure 6 .
Figure 6.Variations of the peak strength and deformation modulus of the borehole specimens with DDRs: (a) Data and fitting curve; (b) Mean change rate.

Figure 9 .
Figure 9. Variations of the peak strengths and deformation moduli of the drilled specimens with different DDHs: (a) Data and fitting curve; (b) Mean change rate.

Figure 12 .
Figure 12.Variations of the peak strength and deformation modulus of drilling specimen with different DSs: (a) Data and fitting curve; (b) Mean change rate.

Figure 13 .
Figure 13.Test data processing diagram for DSs: (a) The peak failure strength ; (b) The deformation modulus

Figure 17 .
Figure 17.Schematic diagram of crack extension direction and maximum principal stress direction: (a) Single drill hole; (b) Multiple holes.

Table 1 .
Natural gradation of sand.

Table 2 .
Mechanical parameters of coal and similar models.

Table 3 .
Scheme design of different drilling diameters (unit: mm).

Table 4 . Experimental results of the peak-failure strength with different DDRs. Specimen number Strength (MPa) Absolute deviation (MPa) Relative deviation (%) Mean value (MPa) Standard deviation (MPa) Coefficientof variation (%)
indicate the mean value of the peak-failure strength of the intact specimen is 5.73 MPa, and the mean value of the deformation modulus is 0.87 GPa.The mean values of the peak-failure strength of the drilled specimens are 4.76 MPa, 4.28 MPa, 3.72 MPa, 3.26 MPa, and the mean values of the deformation

Table 5 .
Experimental results of the deformation modulus with different DDRs.

Table 6 .
Experimental results of the peak-failure strength with different DDHs.

Table 7 .
Experimental results of the deformation modulus with different DDHs.

Table 8 .
Experimental results of the peak-failure strength with different DSs.

Table 9 .
Experimental results of the deformation modulus with different DSs.

Table 10 .
Data on factors influencing the peak-failure strength and deformation modulus of drilled specimens.

Table 11 .
Ranking of the correlations of the influencing factors.